A non-stationary space-time Gaussian Process model for partially converged simulations

In the context of expensive numerical experiments, a promising solution to alleviate the computational costs consists of using partially converged simulations instead of exact solutions. The gain in computational time is at a price of precision in the response. This work addresses the issue of fitting a Gaussian process model to partially converged simulation data, for further use in prediction. The main challenge consists in the adequate approximation of the error due to partial convergence, which is correlated in both design variables and time directions. Here, we propose to fit a Gaussian process in the joint space of design parameters and computational time. The model is constructed by building a non-stationary covariance kernel that reflects accurately the actual structure of the error. Practical solutions are proposed to solve parameter estimation issues associated with the proposed model. The method is applied to a computational fluid dynamics test-case, and shows significant improvement in prediction compared to a classical kriging model. keywords Kriging, computer experiments, covariance kernels